Subgroups — #25067494

Order 11008.

680 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144603	C₂	1	1	yes	maximal, characteristic
2	#19143542	C₂	1	1	yes	maximal, characteristic, complemented
3	#19133483	C₂	1	2	yes	maximal, complemented
4	#19133436	C₂	1	2	yes	maximal, complemented
5	#19133431	C₂	1	2	yes	maximal, complemented
6	C₈×#10621883	C₂	1	2	yes	maximal, complemented
7	#19133367	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133049	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
10	M₁₆×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
12	#14583456	C₂²	1	1	yes	characteristic
13	#14583229	C₄	1	2	yes	—
14	#14583189	C₄	1	1	yes	characteristic
15	#14583189	C₄	1	1	yes	characteristic
16	#14583104	C₄	1	1	yes	characteristic
17	#14583104	C₄	1	1	yes	characteristic
18	#14583050	C₄	1	2	yes	—
19	#14583029	C₂²	1	2	yes	complemented
20	#14583027	—	2	2	no	—
21	C₈×Dic₈₆	C₂²	1	2	yes	complemented
22	C₄×#10621883	C₂²	1	2	yes	—
23	C₄×#10621883	C₂²	1	2	yes	—
24	#14582952	C₂²	1	1	yes	characteristic
25	#14582927	—	2	1	no	—
26	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
27	#14582857	—	2	1	no	—
28	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
29	#14582649	C₂²	1	2	yes	complemented
30	#14582649	C₂²	1	2	yes	complemented
31	#14582629	C₂²	1	2	yes	complemented
32	#14582629	C₂²	1	2	yes	complemented
33	D₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
34	D₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
35	D₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
36	D₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
37	#14582620	C₂²	1	2	yes	complemented
38	C₈×C₄₃⋊C₈	C₂²	1	2	yes	complemented
39	C₂²×M₁₆×C₄₃	—	2	1	no	—
40	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
41	C₄₃×#436	C₂²	1	2	yes	—
42	C₄₃×#435	—	2	2	no	—
43	C₈×D₄×C₄₃	C₂²	1	2	yes	—
44	C₄₃×#423	C₂²	1	1	yes	characteristic
45	C₄₃×#407	—	2	1	no	—
46	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
47	C₂×#10621883	C₂×C₄	1	2	yes	—
48	C₂×#10621883	C₂×C₄	1	2	yes	—
49	C₂²×C₄₃⋊C₈	—	2	1	no	—
50	C₂²×C₄₃⋊C₈	—	2	1	no	—
51	#13063325	C₂×C₄	1	1	yes	characteristic
52	#13063325	C₂×C₄	1	1	yes	characteristic
53	#13063317	—	2	1	no	—
54	#13063304	—	2	1	no	—
55	#13063304	C₂×C₄	1	2	yes	—
56	C₄×Dic₈₆	—	2	1	no	—
57	C₄×Dic₈₆	C₂³	1	2	yes	—
58	#13063284	—	2	1	no	—
59	#13063256	C₂×C₄	1	2	yes	—
60	#13063256	C₂×C₄	1	2	yes	—
61	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
62	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
63	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
64	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
65	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
66	Dic₄₃⋊C₈	—	2	2	no	—
67	Dic₄₃⋊C₈	—	2	2	no	—
68	#13063248	C₂×C₄	1	2	yes	—
69	#13063248	C₂×C₄	1	2	yes	—
70	#13063246	C₂×C₄	1	2	yes	—
71	#13063246	C₂×C₄	1	2	yes	—
72	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
73	#13063235	—	2	2	no	—
74	C₄×C₄₃⋊C₈	—	2	1	no	—
75	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
76	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
77	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
78	C₈×Dic₄₃	—	2	2	no	—
79	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
80	C₂³×C₄×C₄₃	—	2	1	no	—
81	C₂×M₁₆×C₄₃	—	2	1	no	—
82	C₂×M₁₆×C₄₃	—	2	2	no	—
83	C₂×M₁₆×C₄₃	—	4	4	no	—
84	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
85	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
86	C₂²×C₈×C₄₃	—	2	2	no	—
87	C₄×D₄×C₄₃	—	2	1	no	—
88	C₄×D₄×C₄₃	—	2	1	no	—
89	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
90	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
91	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
92	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
95	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₄₃	—	2	1	no	—
97	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
98	C₂²⋊C₈×C₄₃	—	2	2	no	—
99	C₂²⋊C₈×C₄₃	—	2	2	no	—
100	#97×C₄₃	D₄	1	2	yes	—
101	C₄×C₈×C₄₃	C₂³	1	2	yes	—
102	C₂⁴×C₄₃	—	2	1	no	—
103	C₂×D₄×C₄₃	—	2	1	no	—
104	C₂×D₄×C₄₃	—	2	2	no	—
105	C₂×D₄×C₄₃	—	4	1	no	—
106	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	—	2	1	no	—
109	C₂²×C₄×C₄₃	—	2	1	no	—
110	C₂²×C₄×C₄₃	—	2	1	no	—
111	C₂²×C₄×C₄₃	—	2	1	no	—
112	C₂²×C₄×C₄₃	—	2	1	no	—
113	C₂²×C₄×C₄₃	—	4	2	no	—
114	C₂²×C₄×C₄₃	—	4	2	no	—
115	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
118	C₂×Dic₈₆	—	2	1	no	—
119	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
120	M₁₆×C₄₃	—	2	2	no	—
121	M₁₆×C₄₃	—	4	2	no	—
122	M₁₆×C₄₃	—	4	4	no	—
123	M₁₆×C₄₃	SD₁₆	1	4	yes	complemented
124	C₂×C₈×C₄₃	—	2	2	no	—
125	C₂×C₈×C₄₃	—	4	4	no	—
126	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₄₃	—	2	1	no	—
129	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
130	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²⋊C₄×C₄₃	—	2	1	no	—
132	C₂²⋊C₄×C₄₃	—	2	1	no	—
133	C₂²⋊C₄×C₄₃	—	2	1	no	—
134	C₂²⋊C₄×C₄₃	—	2	1	no	—
135	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₄₃	#41	1	1	yes	characteristic
138	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
139	C₂²⋊Dic₄₃	—	2	2	no	—
140	#10621883	—	2	4	no	—
141	#10621883	—	4	2	no	—
142	C₄⋊Dic₄₃	—	2	1	no	—
143	C₄⋊Dic₄₃	—	2	1	no	—
144	C₄⋊Dic₄₃	—	2	1	no	—
145	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
146	Dic₄₃⋊C₄	—	2	2	no	—
147	Dic₄₃⋊C₄	—	2	2	no	—
148	C₄×Dic₄₃	—	2	2	no	—
149	C₂×C₄₃⋊C₈	—	2	1	no	—
150	C₂×C₄₃⋊C₈	—	2	1	no	—
151	C₂×C₄₃⋊C₈	—	2	1	no	—
152	C₂×C₄₃⋊C₈	—	2	1	no	—
153	C₂×C₄₃⋊C₈	—	4	2	no	—
154	C₂×C₄₃⋊C₈	—	4	2	no	—
155	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
156	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
157	C₂³×C₄₃	—	2	1	no	—
158	C₂³×C₄₃	—	2	1	no	—
159	C₂³×C₄₃	—	4	2	no	—
160	C₂³×C₄₃	—	4	2	no	—
161	C₂³×C₄₃	—	8	1	no	—
162	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
163	D₄×C₄₃	—	2	1	no	—
164	D₄×C₄₃	—	2	1	no	—
165	D₄×C₄₃	—	2	1	no	—
166	D₄×C₄₃	—	4	2	no	—
167	D₄×C₄₃	#131	1	2	yes	—
168	C₂×C₄×C₄₃	—	2	1	no	—
169	C₂×C₄×C₄₃	—	2	1	no	—
170	C₂×C₄×C₄₃	—	2	1	no	—
171	C₂×C₄×C₄₃	—	2	1	no	—
172	C₂×C₄×C₄₃	—	4	1	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	—	4	1	no	—
175	C₂×C₄×C₄₃	—	4	1	no	—
176	C₂×C₄×C₄₃	—	4	1	no	—
177	C₂×C₄×C₄₃	—	4	1	no	—
178	C₂×C₄×C₄₃	—	4	2	no	—
179	C₂×C₄×C₄₃	—	4	2	no	—
180	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
184	C₂×C₄×C₄₃	#135	1	2	yes	—
185	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
188	C₂×Dic₄₃	—	2	2	no	—
189	C₂×Dic₄₃	—	2	2	no	—
190	Dic₈₆	—	2	2	no	—
191	Dic₈₆	—	2	2	no	—
192	Dic₈₆	—	8	1	no	—
193	C₈×C₄₃	—	2	2	no	—
194	C₈×C₄₃	—	4	2	no	—
195	C₈×C₄₃	C₂×SD₁₆	1	4	yes	—
196	C₄₃⋊C₈	—	2	2	no	—
197	C₄₃⋊C₈	—	2	2	no	—
198	C₄₃⋊C₈	—	2	2	no	—
199	C₄₃⋊C₈	—	4	1	no	—
200	C₄₃⋊C₈	—	4	1	no	—
201	C₄₃⋊C₈	—	4	1	no	—
202	#17995	—	43	1	no	maximal, Sylow
203	C₂²×C₄₃	—	2	1	no	—
204	C₂²×C₄₃	—	2	1	no	—
205	C₂²×C₄₃	—	2	2	no	—
206	C₂²×C₄₃	—	4	1	no	—
207	C₂²×C₄₃	—	4	1	no	—
208	C₂²×C₄₃	—	4	1	no	—
209	C₂²×C₄₃	—	4	1	no	—
210	C₂²×C₄₃	—	4	1	no	—
211	C₂²×C₄₃	—	8	4	no	—
212	C₂²×C₄₃	C₄×SD₁₆	1	2	yes	—
213	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
214	C₄×C₄₃	—	2	1	no	—
215	C₄×C₄₃	—	2	1	no	—
216	C₄×C₄₃	—	2	1	no	—
217	C₄×C₄₃	—	4	1	no	—
218	C₄×C₄₃	—	4	1	no	—
219	C₄×C₄₃	C₄×SD₁₆	1	2	yes	—
220	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
221	C₄×C₄₃	#568	1	1	yes	characteristic
222	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
223	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
224	Dic₄₃	—	4	2	no	—
225	Dic₄₃	—	4	2	no	—
226	#3101	—	43	1	no	—
227	#2962	—	43	1	no	—
228	D₄×M₁₆	D₄₃	1	1	yes	characteristic
229	#1590	—	43	2	no	—
230	#1583	—	43	2	no	—
231	#1582	—	43	2	no	—
232	C₈×SD₁₆	—	43	2	no	—
233	#1570	—	43	1	no	—
234	#1493	—	43	1	no	—
235	C₂×D₄⋊C₈	—	43	1	no	—
236	C₈×M₁₆	—	43	1	no	—
237	C₂×C₄₃	—	2	2	no	—
238	C₂×C₄₃	—	4	2	no	—
239	C₂×C₄₃	—	8	1	no	—
240	C₂×C₄₃	#2933	1	1	yes	characteristic
241	C₂×C₄₃	C₂×C₄×SD₁₆	1	1	yes	characteristic
242	C₂×C₄₃	#2956	1	1	yes	characteristic
243	C₂²×M₁₆	—	2	1	no	—
244	#533	—	43	1	no	—
245	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
246	#483	—	43	2	no	—
247	#476	—	43	1	no	—
248	#476	—	43	1	no	—
249	#461	—	43	1	no	—
250	#461	—	43	1	no	—
251	#450	—	43	2	no	—
252	#446	—	43	2	no	—
253	#446	—	86	2	no	—
254	C₈×Q₈	—	43	2	no	—
255	C₄×SD₁₆	—	43	2	no	—
256	C₄×SD₁₆	—	43	2	no	—
257	#436	C₂×D₄₃	1	2	yes	—
258	#435	—	2	2	no	—
259	C₈×D₄	C₂×D₄₃	1	2	yes	—
260	#431	—	43	1	no	—
261	#424	—	86	1	no	—
262	#423	C₂×D₄₃	1	1	yes	characteristic
263	C₂×C₄⋊C₈	—	43	1	no	—
264	#407	—	2	1	no	—
265	#405	—	86	1	no	—
266	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
267	C₂×C₄×C₈	—	43	1	no	—
268	#334	—	43	2	no	—
269	#334	—	43	2	no	—
270	Q₈⋊C₈	—	43	2	no	—
271	Q₈⋊C₈	—	43	2	no	—
272	D₄⋊C₈	—	43	1	no	—
273	D₄⋊C₈	—	43	1	no	—
274	D₄⋊C₈	—	43	1	no	—
275	D₄⋊C₈	—	43	1	no	—
276	#322	—	43	2	no	—
277	C₈²	—	43	2	no	—
278	C₄₃	#17995	1	1	yes	characteristic, complemented, Sylow
279	C₂²×D₄	C₄×D₄₃	1	1	yes	characteristic
280	C₂³×C₄	—	2	1	no	—
281	C₂×SD₁₆	—	43	2	no	—
282	C₂×SD₁₆	—	43	2	no	—
283	C₂×M₁₆	—	2	1	no	—
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	—	4	4	no	—
286	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
287	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
288	C₂²×C₈	—	2	2	no	—
289	C₂²×C₈	—	86	1	no	—
290	C₂²×C₈	—	86	1	no	—
291	C₄⋊Q₈	—	43	1	no	—
292	C₄⋊Q₈	—	43	1	no	—
293	#125	—	86	1	no	—
294	C₂²⋊Q₈	—	43	2	no	—
295	C₂²⋊Q₈	—	86	1	no	—
296	C₄×Q₈	—	43	2	no	—
297	C₄×Q₈	—	86	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	C₄×D₄₃	1	1	yes	characteristic
301	C₄×D₄	C₄×D₄₃	1	1	yes	characteristic
302	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
303	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
304	#117	—	86	1	no	—
305	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
308	#106	—	43	2	no	—
309	#106	—	43	2	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	43	1	no	—
312	C₄⋊C₈	—	43	1	no	—
313	C₄⋊C₈	—	43	1	no	—
314	C₄⋊C₈	—	43	1	no	—
315	C₄⋊C₈	—	86	2	no	—
316	C₄⋊C₈	—	86	2	no	—
317	C₄⋊C₈	—	86	1	no	—
318	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
319	#103	—	43	2	no	—
320	#103	—	43	2	no	—
321	#102	—	43	2	no	—
322	#102	—	43	2	no	—
323	C₂²⋊C₈	—	2	2	no	—
324	C₂²⋊C₈	—	2	2	no	—
325	C₂²⋊C₈	—	43	2	no	—
326	#97	—	86	2	no	—
327	#97	C₂²⋊D₄₃	1	2	yes	—
328	C₄×C₈	—	43	2	no	—
329	C₄×C₈	—	43	1	no	—
330	C₄×C₈	—	43	1	no	—
331	C₄×C₈	—	86	2	no	—
332	C₄×C₈	—	86	1	no	—
333	C₄×C₈	C₂²×D₄₃	1	2	yes	—
334	C₂⁴	—	2	1	no	—
335	C₂×Q₈	—	43	2	no	—
336	C₂×Q₈	—	86	1	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
341	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
350	C₂²×C₄	#10621898	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
352	SD₁₆	—	86	4	no	—
353	SD₁₆	—	172	2	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	4	2	no	—
356	M₁₆	—	4	4	no	—
357	M₁₆	#10621883	1	4	yes	complemented
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	4	4	no	—
360	C₂×C₈	—	43	2	no	—
361	C₂×C₈	—	43	2	no	—
362	C₂×C₈	—	86	1	no	—
363	C₂×C₈	—	86	1	no	—
364	C₂×C₈	—	86	1	no	—
365	C₂×C₈	—	86	1	no	—
366	C₂×C₈	—	172	2	no	—
367	C₂×C₈	—	172	2	no	—
368	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
369	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	43	2	no	—
372	C₄⋊C₄	—	86	1	no	—
373	C₄⋊C₄	—	86	1	no	—
374	C₄⋊C₄	—	86	2	no	—
375	C₄⋊C₄	—	86	1	no	—
376	C₄⋊C₄	—	86	2	no	—
377	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
378	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
379	C₂²⋊C₄	—	2	1	no	—
380	C₂²⋊C₄	—	2	1	no	—
381	C₂²⋊C₄	—	2	1	no	—
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	86	2	no	—
384	C₄²	—	86	2	no	—
385	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
386	C₄²	#10621898	1	1	yes	characteristic
387	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
388	C₄²	C₂³×D₄₃	1	1	yes	characteristic
389	C₂³	—	2	1	no	—
390	C₂³	—	2	1	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	8	1	no	—
394	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
395	Q₈	—	86	2	no	—
396	Q₈	—	86	2	no	—
397	Q₈	—	344	1	no	—
398	D₄	—	2	1	no	—
399	D₄	—	2	1	no	—
400	D₄	—	2	1	no	—
401	D₄	—	4	2	no	—
402	D₄	#13063333	1	2	yes	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	86	2	no	—
416	C₂×C₄	—	86	2	no	—
417	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
418	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
419	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
420	C₂×C₄	C₂×#10621883	1	2	yes	—
421	C₂×C₄	#13063345	1	2	yes	—
422	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
424	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	4	2	no	—
427	C₈	—	86	2	no	—
428	C₈	—	86	2	no	—
429	C₈	—	86	2	no	—
430	C₈	—	172	1	no	—
431	C₈	—	172	1	no	—
432	C₈	—	172	1	no	—
433	C₈	C₂×#10621883	1	4	yes	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	8	4	no	—
443	C₂²	C₄×#10621883	1	2	yes	—
444	C₂²	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	4	1	no	—
449	C₄	—	4	1	no	—
450	C₄	—	172	2	no	—
451	C₄	—	172	2	no	—
452	C₄	C₄×#10621883	1	2	yes	—
453	C₄	C₂×#13063333	1	1	yes	characteristic
454	C₄	#14583665	1	1	yes	characteristic
455	C₄	C₂²×#10621883	1	1	yes	characteristic
456	C₄	C₂×#13063345	1	1	yes	characteristic
457	C₂	—	2	2	no	—
458	C₂	—	4	2	no	—
459	C₂	—	8	1	no	—
460	C₂	#19143320	1	1	yes	characteristic
461	C₂	C₂×C₄×#10621883	1	1	yes	characteristic
462	C₂	#19143502	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	D₄×M₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂²×D₄×C₄₃	C₂×C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	D₄×M₁₆	D₄₃
hypocenter	C₄₃	#17995
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ D₄×M₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #19143542	C₂	semidirect
3. #19133483	C₂	semidirect
4. #19133436	C₂	semidirect
5. #19133431	C₂	semidirect
6. C₈×#10621883	C₂	semidirect
7. #19133367	C₂	semidirect
8. #19133049	C₂	semidirect
10. M₁₆×C₄₃⋊C₈	C₂	semidirect
19. #14583029	C₂²	semidirect
21. C₈×Dic₈₆	C₂²	semidirect
29. #14582649	C₂²	semidirect
30. #14582649	C₂²	semidirect
31. #14582629	C₂²	semidirect
32. #14582629	C₂²	semidirect
37. #14582620	C₂²	semidirect
38. C₈×C₄₃⋊C₈	C₂²	semidirect
123. M₁₆×C₄₃	SD₁₆	semidirect
278. C₄₃	#17995	semidirect
357. M₁₆	#10621883	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#19144603	2
#19143542	2
#19133483	2
#19133436	2
#19133431	2
C₈×#10621883	2
#19133367	2
#19133049	2
C₂×D₄⋊(C₄₃⋊C₈)	2
M₁₆×C₄₃⋊C₈	2
D₄×M₁₆×C₄₃	2
#17995	43